In how many ways can the letters of the following words be arranged:
RADIO

Answer

To find the number of ways to arrange the letters of the word "RADIO", we can follow these steps:

### Step 1: Count the total number of letters
The word "RADIO" consists of 5 distinct letters: R, A, D, I, O.

### Step 2: Use the formula for permutations
Since all the letters are distinct, we can use the formula for permutations of n distinct objects, which is given by n! (n factorial).

### Step 3: Calculate the factorial
Here, n = 5 (the number of letters in "RADIO"). Therefore, we need to calculate 5! (5 factorial).

5! = 5 × 4 × 3 × 2 × 1

### Step 4: Perform the multiplication
Calculating this gives us:

5! = 5 × 4 = 20
20 × 3 = 60
60 × 2 = 120
120 × 1 = 120

### Step 5: Conclusion
Thus, the total number of ways to arrange the letters of the word "RADIO" is 120.

### Final Answer:
The number of ways to arrange the letters of the word "RADIO" is **120**.

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